Video: Solving One-Step Linear Equations in Real-World Contexts

The distance 𝑑 Scarlett travels in her car while driving 58 miles per hour for 1.5 hours is given by the equation 𝑑/1.5 = 58. How far did she travel?

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Video Transcript

The distance 𝑑 Scarlett travels in her car while driving 58 miles per hour for 1.5 hours is given by the equation 𝑑 over 1.5 equals 58. How far did she travel?

So, the equation that we’ve been given 𝑑 over 1.5 equals 58 contains all the other information that we’ve been given. Because it tells us that Scarlett has been driving at 58 miles per hour, well, that’s part of our equation, and it tells us that she’s been driving for 1.5 hours. That’s also in our equation. So, what we need to do is rearrange our equation to solve to find 𝑑.

So, what our equation tells us is that 𝑑 divided by 1.5 is equal to 58. Well, if we want to find 𝑑 and we’ve got 𝑑 divided by 1.5, then what we need to do is multiply it by 1.5. And then, we’d just be left with 𝑑. However, whatever we do to one side of the equation we must do to the other side of the equation. So, what we’re gonna do is multiply both sides of our equation by 1.5.

So, what we’re gonna get is 𝑑 is equal to. And now we can work out the right-hand side of the equation. So, what I’m gonna do is split up the calculation to work it out. So, first we’re gonna have one multiplied by 58, which is just equal to 58. So then, we’re gonna have 0.5 multiplied by 58. And that’s because we want 1.5 multiplied by 58, so we can divide it into two parts, one and then 0.5.

Now to carry out this calculation, what we’re gonna do is divide 58 by two. Well, we can do that mentally. Or we can also use the bus stop method. So, to use the bus stop method, we see how many twos go into five. Well, twos into five go two because two multiplied by two is four remainder one. And then, we’re gonna see how many twos go into 18 cause we carry the one. And that is nine. So, we can see that 58 divided by two is 29. So, now we have 58 and 29. So, what we do is we add these together.

So, first of all, we have eight add nine, which gives us 17. So, we have a seven, and then we carry the one. And then, we have one add five, which is six, add two, which is eight. So, we get 87. So, we can say that 1.5 multiplied by 58 is 87. So therefore, we can say that 𝑑 equals 87. And if we take a look back at the question, we can see that the unit is gonna be miles. So therefore, we can say that the distance 𝑑 Charlotte [Scarlett] travels in her car while driving 58 miles per hour for 1.5 hours is 87 miles.

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